Part A -
Q1. A study comparing attitudes toward death was conducted in which organ donors (individuals who had signed organ donor cards) were compared with nondonors. The study is reported in the journal Death Studies. Tempter's Death Anxiety Scale (DAS) was administered to both groups. On this scale, high scores indicate high anxiety concerning death. The results were reported as follows.
|
|
n
|
Mean
|
Std. Dev.
|
|
Organ Donors
|
25
|
5.36
|
2.91
|
|
Non-organ Donors
|
69
|
7.62
|
3.45
|
Construct the 95% confidence interval for the difference between the means, μnon - μdonor.
Q2. Women on average have 8 more pairs of shoes than do men, according to a USA Today Snapshot titled "Who Owns More Shoes?" (July 8, 2009). A recent study at a community college gave the following results:
|
|
n
|
Mean
|
Std. Dev.
|
|
Males
|
21
|
8.48
|
4.43
|
|
Females
|
30
|
26.63
|
21.83
|
Find the 90% confidence interval for the difference between the two mean numbers of pairs of shoes for males and females.
Q3. At a large university, a mathematics placement exam is administered to all students. Samples of 36 male and 30 female students are randomly selected from this year's student body and the following scores recorded:
|
Male
|
72
|
68
|
75
|
82
|
81
|
60
|
75
|
85
|
80
|
70
|
|
|
71
|
84
|
68
|
85
|
82
|
80
|
54
|
81
|
86
|
79
|
|
|
99
|
900
|
68
|
82
|
60
|
63
|
67
|
72
|
77
|
51
|
|
|
61
|
71
|
81
|
74
|
79
|
76
|
|
|
|
|
|
Female
|
81
|
76
|
94
|
89
|
83
|
78
|
85
|
91
|
83
|
83
|
|
|
84
|
80
|
84
|
88
|
77
|
74
|
63
|
69
|
80
|
82
|
|
|
89
|
69
|
74
|
97
|
73
|
79
|
55
|
76
|
78
|
81
|
Construct the 95% confidence interval for the difference between the mean scores for male and female students.
Q4. State the null and alternative hypotheses that would be used to test the following claims:
a. There is a difference between the mean age of employees at two different large companies.
b. The mean of population 1 is greater than the mean of population 2.
c. The mean yield per county of sunflower seeds in North Dakota is less than the mean yield per county in South Dakota.
d. The is no difference in the mean number of hours spent studying per week between male and female college students.
Q5. It is a known fact that private colleges cost more than public colleges. In fact, according to the College Board, the average 2008-2009 cost (tuition, fees, room & board) for a public college is $7,020 versus $26,273 for a private college. Does this difference hold when it comes to the average cost of required textbooks per class? The following samples of size 10 were taken.
|
Public
|
Private
|
|
64.69
|
71.00
|
|
89.60
|
96.19
|
|
101.49
|
96.47
|
|
101.75
|
97.14
|
|
103.59
|
98.56
|
|
106.38
|
98.94
|
|
106.77
|
107.79
|
|
110.69
|
112.58
|
|
118.94
|
114.00
|
|
135.94
|
116.55
|
Using the Excel output below and α = 0.05, determine if the average cost of required textbooks per class is different between public and private colleges.
a. Solve using the p-value approach.
b. Solve using the classical approach.
Part B -
Q1. If n1 = 40, p'1 = 0.9, n2 = 50, and p'2 = 0.9:
a. Find the estimated values for both np's and both nq's.
b. Would this situation satisfy the guidelines for approximately normal? Explain.
Q2. Calculate the estimate for the standard error of the difference between two proportions for each of the following cases:
a. n1 = 40, p'1 = 0.8, n2 = 50, and p'2 = 0.8
b. n1 = 33, p'1 = 0.6, n2 = 38, and p'2 = 0.65
Q3. The proportions of defective parts produced by two machines were compared, and the following data were collected:
Machine 1: n = 150; number of defective parts = 12
Machine 2: n = 150: number of defective parts = 6
Determine a 90% confidence interval for p1 - p2.
Q4. The Soap and Detergent Association issued its fifth annual Clean Hands Report Card survey for 2009. In a series of hygiene-related questions to American adults, it was found that 62% of 442 women washed their hands more than 10 times per day, while 37% of 446 men did the same. Find the 95% confidence interval for the difference in proportions of women and men that wash their hands more than 10 times a day.
Q5. In a random sample of 40 brown-haired individuals, 22 indicated that they use hair coloring. In another random sample of 40 blond individuals, 26 indicated that they use hair coloring. Use a 92% confidence interval to estimate the difference in the population proportions of brunettes and blondes who use hair coloring.
Q6. State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims:
a. There is no difference between the proportions of men and women who will vote for the incumbent in next month's election.
b. The percentage of boys who cut classes is greater than the percentage of girls who cut classes.
c. The percentage of college students who drive old cars is higher than the percentage of noncollege students of the same age who drive old cars.